Updating GameObject Variables in Script

I've done a lot of searching on this topic and can't find the answer to my question. It may be something obvious but I am relatively new to Unity, coming from a strong background in other programming languages/environments.

This issue I have is how do you modify or work with a game object's variables or functions through the script that is attached to it. I.E. lets say I have a music volume slider. I know that if I want to update the stored volume value I can do the following:

 private void Update ()
     {
         GameManager.Instance.music_volume = music_slider.value;
     }

The above works fine for storing the value from the slider into my game manager singleton class which then updates the user player preferences. This issue I can't wrap my head around is how do I get "music_slider" to reference the Slider Game Object that the script is attached to.

This has been my solution so far but it just doesn't feel right, any suggestions?

 private Slider music_slider;    // Internal Slider Reference

 private void Awake()
 {
     // Internal slider reference is always to the Slider Game Object that the script is attached to.
     music_slider = this.gameObject.GetComponent<Slider>();
 }

For complete clarity here is the full structure of my script class that is attached to a MusicVolumeSlider

 public class MusicSliderControl : MonoBehaviour
 {
     private Slider music_slider;    // Internal Slider Reference

     private void Awake()
     {
         // Internal slider reference is always to the Slider Game Object that the script is attached to.
         music_slider = this.gameObject.GetComponent<Slider>();
     }

     // Use this for initialization
     private void Start ()
     {
         music_slider.value = GameManager.Instance.music_volume;
     }
 
     // Update is called once per frames
     private void Update ()
     {
         GameManager.Instance.music_volume = music_slider.value;
     }
 }